All of the 3rd grade teachers and students from Gardner Bullis went on a field trip to an art museum. Tickets were $$6.00$ each for teachers and $$4.50$ each for students, and the group paid $$30.00$ in total. The next month, the same group visited a science museum where the tickets cost $$24.00$ each for teachers and $$11.50$ each for students, and the group paid $$94.00$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${6x+4.5y = 30}$ ${24x+11.5y = 94}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-24x-18y = -120}$ ${24x+11.5y = 94}$ Add the top and bottom equations together. $ -6.5y = -26 $ $ y = \dfrac{-26}{-6.5}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $ {6x+4.5y = 30}$ to find $x$ ${6x + 4.5}{(4)}{= 30}$ $6x+18 = 30$ $6x = 12$ $x = \dfrac{12}{6}$ ${x = 2}$ You can also plug ${y = 4}$ into $ {24x+11.5y = 94}$ and get the same answer for $x$ ${24x + 11.5}{(4)}{= 94}$ ${x = 2}$ There were $2$ teachers and $4$ students on the field trips.